Postgres ENUM data type or CHECK CONSTRAINT?

I have been migrating a MySQL db to Pg (9.1), and have been emulating MySQL ENUM data types by creating a new data type in Pg, and then using that as the column definition. My question -- could I, and would it be better to, use a CHECK CONSTRAINT instead? The MySQL ENUM types are implemented to enforce specific values entries in the rows. Could that be done with a CHECK CONSTRAINT? and, if yes, would it be better (or worse)?